About shrinkwrap - Any way to apply it to a vertex group and move the rest the proportional distance?
Instead of a subdivided plane, use a subdivided edge like so :

Add your shrinkwrap :

Now add a Screw Modifier set to Z axis, angle 0°, with 1 step and tweak the screw value:

Moving the source object along the X Axis :

You can add a solidify modifier after all this to add thickness to your wall :